About half my missions are MiB missions.
This is very strange. Maybe MiB missions got generated next to each other so you're having a period of high frequency, but the overall proportion should be about 25%MiB/75%aliens.
At least the latest version I'm quite sure it is not 50/50.
The problem is, testing this takes tons, tons of time (running numerous campaigns and taking notice of the missions): I don't have it.
The MiB base looks like a landed UFO that stays there for a long time (2 years IIRC). And technically IS a UFO, so you're not getting any message or mark unless your radar spots it. If one exists somewhere in the world, you should be able to spot it by patrolling over it with your crafts. There will be a base at some point in time, it's guaranteed.