EPW produces two separate gaps at one k-point

[CHILLL]

Dear experts and users,

I have performed an EPW calculation on a 2D material, and there is something that puzzles me about the result.
The Fermi surface of my material has contributions from two types of states :px/py and pz. The situation is more or less like MgB2, but there is one big difference: the sheets are not separate but quite tangled. Particularly, they have several crossing points at the Fermi level.
After running EPW I see that the code produced absolutely separate gaps for px/py and pz. So, basically at the same k-point(where the two bands cross) I have two separate gaps. Is this possible? Intuitively, I would say that these 2 gaps have to be hybridised somehow. Also, by analysing \lambda_{q,\nu} I can see that there are modes that are strongly coupled at Gamma point, shouldn't these modes then add some interband behaviour to the picture?

To illustrate the problem, I paste here what I see in the "imag_aniso_gap_FS" file:
# k-point Band Enk-Ef [eV] Delta(0) [eV]
...
0.059524 0.323041 0.000000 1 0.009315 0.001205904154834
0.059524 0.323041 0.000000 2 0.017310 0.000779521241412
...

So, as you can see, Identical k-points give very distinct gap values, which look like two separate peaks when I plot the gap distribution.

Thank you!
Mikhail