Does Mexico even have an airforce? Do they field any combat-capable
aircraft, or is it just non-combatant types like search and rescue or
cargo planes?

According to the news
http://www.wired.com/news/technology...w=wn_1techhead
the Mexican Air Force spotted unidentified "UFO" bright objects.

Or a more humorous take on the subject
http://www.ridiculopathy.com/news_detail.php?id=1075