We are not self employed, but we did purchase insurance through the marketplace for my ILs (they moved here 2.5 years ago from Eastern Europe). In their case it was a little complicated to verify their identities (we needed to get them state IDs, as their green cards were not sufficient). But once that was all set up, it was easy. There is a range of competency when you call to talk to people. (We did have private insurance for them for 1/2 a year at first and it was significantly more expensive than going through the marketplace, and we don't think there's any difference in ease/coverage.)
DD (3/06)
DS1 (7/09)
DS2 (8/13)