My experience is v similar to hauteboy's - I just recently flew MEX-HAV-CUN-MEX.

At MEX, I was able to use the MexicanaElite check-in area and was invited to use the international lounge (which incidentally is v small and has limited snacks/booze). Would recommend using the Admiral's Club one level down. On boarding, J and Mexicana/oneworld shiny card holders were invited to board at lesiure.

At HAV, there was no elite check-in facility as I was flying on MexicanaLink (and oh god I'd forgotten how much fun standing for ages in a check-in queue isn't). There is a shared VIP lounge but I didn't bother checking it out. No offer of early boarding, but it was a small plane (F100) so not too much of an issue in any case.

At CUN, I was able to use the elite check-in queue to get my bag re-tagged and was then invited to use the (miniscule) lounge. No better lounging facilities that I was aware of, but it was a fairly short layover so no real complaints. Would hate to have to spend more than an hour or so there, though. I don't remember any offers of priority boarding.

It was the first time I'd flown on MX and would v happily fly them again. Good service on the ground and on board -- considering the flights were relatively short, I was quite happy to receive some food to munch on and a full bar service to keep my liver entertained