Combining scatter plot with surface plot

How can I combine a 3D scatter plot with a 3D surface plot while keeping the surface plot transparent so that I can still see all the points?

The following code plots a 3D scatter plot with a 3D surface plot:

import matplotlib.pyplot as plt
import numpy as np
from random import random, seed
from matplotlib import cm
import matplotlib as mpl

fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(projection='3d')              # to work in 3d

x_surf=np.arange(0, 1, 0.01)                # generate a mesh
y_surf=np.arange(0, 1, 0.01)
x_surf, y_surf = np.meshgrid(x_surf, y_surf)
z_surf = np.sqrt(x_surf+y_surf)             # ex. function, which depends on x and y
ax.plot_surface(x_surf, y_surf, z_surf, cmap=cm.hot, ec='k')  # plot a 3d surface plot

n = 100
seed(0)                                     # seed let us to have a reproducible set of random numbers
x=[random() for i in range(n)]              # generate n random points
y=[random() for i in range(n)]
z=[random() for i in range(n)]
ax.scatter(x, y, z);                        # plot a 3d scatter plot

ax.set_xlabel('x label')
ax.set_ylabel('y label')
ax.set_zlabel('z label')

plt.show()

You can see some other examples with 3d plots here.

I've changed the colors of the surface plot from the default to a colormap hot, in order to distinguish the colors of the two plots - now, it's seen that the surface plot overrides the scatter plot, independently of the order.

To fix that issue, it should be used transparency in the colormap of the surface plot; adding the code from Transparent colormap

and changing the line:

ax.plot_surface(x_surf, y_surf, z_surf, cmap=cm.hot)  # plot a 3d surface plot

to

theCM = mpl.colormaps.get_cmap('bwr')
theCM._init()
alphas = np.abs(np.linspace(-1.0, 1.0, theCM.N))
theCM._lut[:-3,-1] = alphas

# other code

ax.plot_surface(x_surf, y_surf, z_surf, cmap=theCM)