ListPlot3D can't plot data of an almost vertical surface?

Question

I have two sets of data. data1, boundary points of the two yellow surfaces shown below, are correctly plotted. However, data2, points almost in the vertical $y=0$-plane, do not show up. data2 is more or less like that the two leaves of data1 close and coincide in the $y=0$-plane.

I want to show both data sets together (Edit: and their colors chosen automatically by PlotTheme -> "Business" as they're normally rendered). Is there any way out?

ListPlot3D[{data1, data2}, PlotRange -> {{-0.5, 0.5}, {-0.1, 0.1}, {0, 0.1}}, PlotTheme -> "Business", AxesLabel -> {x, y, z}]

The data are as follows

{data1, data2}={{{-0.498888, -3.19621*10^-25, 0.0333333}, {-0.473122, -0.00470247, 
   0.0363173}, {-0.403804, -0.0176968, 
   0.0445669}, {-0.301622, -0.0371004, 
   0.0568813}, {-0.150161, -0.0618223, 
   0.0724944}, {0.0848717, -0.0741708, 
   0.0794865}, {0.275171, -0.0567612, 
   0.0671902}, {0.378431, -0.0384026, 
   0.0551864}, {0.431566, -0.0254112, 
   0.0471327}, {0.458987, -0.0170245, 
   0.0421882}, {0.473576, -0.0117328, 
   0.0392161}, {0.481711, -0.00837124, 
   0.0374124}, {0.486505, -0.00618227, 
   0.0362863}, {0.489508, -0.00469733, 
   0.0355513}, {0.491537, -0.00362577, 
   0.0350384}, {0.493065, -0.00278219, 
   0.0346445}, {0.494405, -0.00204806, 
   0.0343046}, {0.495751, -0.00136093, 
   0.0339839}, {0.497136, -0.000724309, 
   0.0336822}, {0.498332, -0.000221891, 
   0.0334408}, {0.498885, -1.20715*10^-6, 0.0333339}, {-0.498888, 0., 
   0.0333333}, {-0.473122, 0., 0.0333333}, {-0.403804, 0., 
   0.0333333}, {-0.301622, 0., 0.0333333}, {-0.150161, 0., 
   0.0333333}, {0.0848717, 0., 0.0333333}, {0.275171, 0., 
   0.0333333}, {0.378431, 0., 0.0333333}, {0.431566, 0., 
   0.0333333}, {0.458987, 0., 0.0333333}, {0.473576, 0., 
   0.0333333}, {0.481711, 0., 0.0333333}, {0.486505, 0., 
   0.0333333}, {0.489508, 0., 0.0333333}, {0.491537, 0., 
   0.0333333}, {0.493065, 0., 0.0333333}, {0.494405, 0., 
   0.0333333}, {0.495751, 0., 0.0333333}, {0.497136, 0., 
   0.0333333}, {0.498332, 0., 0.0333333}, {0.498885, 0., 
   0.0333333}, {-0.498888, 3.19621*10^-25, 0.0333333}, {-0.473122, 
   0.00470247, 0.0363173}, {-0.403804, 0.0176968, 
   0.0445669}, {-0.301622, 0.0371004, 0.0568813}, {-0.150161, 
   0.0618223, 0.0724944}, {0.0848717, 0.0741708, 
   0.0794865}, {0.275171, 0.0567612, 0.0671902}, {0.378431, 0.0384026,
    0.0551864}, {0.431566, 0.0254112, 0.0471327}, {0.458987, 
   0.0170245, 0.0421882}, {0.473576, 0.0117328, 0.0392161}, {0.481711,
    0.00837124, 0.0374124}, {0.486505, 0.00618227, 
   0.0362863}, {0.489508, 0.00469733, 0.0355513}, {0.491537, 
   0.00362577, 0.0350384}, {0.493065, 0.00278219, 
   0.0346445}, {0.494405, 0.00204806, 0.0343046}, {0.495751, 
   0.00136093, 0.0339839}, {0.497136, 0.000724309, 
   0.0336822}, {0.498332, 0.000221891, 0.0334408}, {0.498885, 
   1.20715*10^-6, 0.0333339}}, {{-0.498888, -9.72703*10^-25, 
   0.0333333}, {-0.456846, -1.51447*10^-18, 
   0.037797}, {-0.354429, -5.33941*10^-18, 
   0.0490817}, {-0.220841, -1.05463*10^-17, 
   0.0644295}, {-0.0421324, -1.62937*10^-17, 
   0.0810826}, {0.163827, -1.57394*10^-17, 
   0.0781084}, {0.295344, -1.19327*10^-17, 
   0.0660401}, {0.371789, -8.73286*10^-18, 
   0.0564082}, {0.41643, -6.41942*10^-18, 
   0.0497166}, {0.443037, -4.80383*10^-18, 
   0.0452114}, {0.459355, -3.67756*10^-18, 
   0.0421786}, {0.4697, -2.88168*10^-18, 
   0.0401073}, {0.4765, -2.30525*10^-18, 
   0.038657}, {0.481163, -1.8717*10^-18, 
   0.0376029}, {0.484553, -1.52674*10^-18, 
   0.0367919}, {0.487254, -1.22976*10^-18, 
   0.0361134}, {0.489711, -9.49526*10^-19, 
   0.0354838}, {0.492259, -6.65265*10^-19, 
   0.0348463}, {0.495015, -3.7648*10^-19, 
   0.0341936}, {0.49759, -1.23131*10^-19, 
   0.0336157}, {0.49888, -7.01073*10^-22, 0.0333349}, {-0.498888, 0., 
   0.0333333}, {-0.456846, 0., 0.0333333}, {-0.354429, 0., 
   0.0333333}, {-0.220841, 0., 0.0333333}, {-0.0421324, 0., 
   0.0333333}, {0.163827, 0., 0.0333333}, {0.295344, 0., 
   0.0333333}, {0.371789, 0., 0.0333333}, {0.41643, 0., 
   0.0333333}, {0.443037, 0., 0.0333333}, {0.459355, 0., 
   0.0333333}, {0.4697, 0., 0.0333333}, {0.4765, 0., 
   0.0333333}, {0.481163, 0., 0.0333333}, {0.484553, 0., 
   0.0333333}, {0.487254, 0., 0.0333333}, {0.489711, 0., 
   0.0333333}, {0.492259, 0., 0.0333333}, {0.495015, 0., 
   0.0333333}, {0.49759, 0., 0.0333333}, {0.49888, 0., 0.0333333}}};

Answer 1

Update: To have the colors in the two plots match the colors in a single plot with PlotTheme -> "Business":

colors = "DefaultPlotStyle" /. Method /. Charting`ResolvePlotTheme["Business", ListPlot3D]);

Show[ListPlot3D[data1, PlotTheme -> "Business"], 
 MapAt[10^-17 # &, #, {1, 1, 1, All, 2}] &@
  ListPlot3D[MapAt[10^17 # &, data2, {All, 2}], PlotRange -> All, 
   PlotStyle -> colors[[2]], PlotTheme -> "Business"], 
 ImageSize -> Large, ViewPoint -> {3, 1, 1.5}]

Original answer:

You can (1) scale the second column of data2 (so that it is not almost constant), (2) use ListPlot3D and (3) post-process to reverse the scaling:

Show[ListPlot3D[data1], 
 ListPlot3D[MapAt[10^17 # &, data2, {All, 2}], PlotRange -> All] /. 
  GraphicsComplex[a_, b___] :> GraphicsComplex[MapAt[10^-17 # &, a, {All, 2}], b], 
 ImageSize -> Large, ViewPoint -> {3, 1, 1.5}]

Or

Show[ListPlot3D[data1], 
 MapAt[10^-17 # &, #, {1, 1, 1, All, 2}] &@
  ListPlot3D[MapAt[10^17 # &, data2, {All, 2}], PlotRange -> All], 
 ImageSize -> Large, ViewPoint -> {3, 1, 1.5}]

same picture

Alternatively, plot data2 with the option ScalingFunctions -> {None, {10^17 # &, 10^-17 # &}, None} and post-process the output to undo the scaling:

Show[ListPlot3D[data1], 
  MapAt[10^-17 # &, #, {1, 1, 1, All, 2}] &@
   ListPlot3D[data2, ScalingFunctions -> {None, {10^17 # &, 10^-17 # &}, None}, 
    PlotRange -> All], 
 ImageSize -> Large, ViewPoint -> {3, 1, 1.5}]

same picture

Note: For version 11.3 (Windows 10) use MapAt[10^-17 # &, #, {1, 1, All, 2}] &.

Answer 2

We can convert Polygon to MeshRegion and then plot it with RegionPlot3D:

Show[ListPlot3D[data1], RegionPlot3D[DiscretizeGraphics[Polygon[data2]], Mesh -> 10]]