Meaning of undergraduate, graduate or post-graduate in US
Part of the confusion may be that these adjectives are used in (at least) two different contexts: to describe degrees and to describe students.


An undergraduate degree generally means a bachelor's degree (B.S., B.A., etc): a degree requiring about four years of university-level study beyond high school.
A graduate degree or post-graduate degree is any higher degree that has a bachelor's degree as a prerequisite, such as a masters or doctoral degree (M.S., M.A., M.F.A., M.B.A,. Ph.D., etc.)  Depending on context, this term may also include professional degrees (J.D. for law, M.D. for medicine, D.D.S. for dentistry, D.V.M. for veterinary medicine, etc).
An undergraduate student (or simply an undergraduate, or colloquially, an undergrad) is a student who does not yet have an undergraduate degree, but is studying to earn one.
A graduate student or post-graduate student (or colloquially, a grad student) is a student who already has an undergraduate degree and is studying to earn a graduate degree.


So in general, the adjectives graduate and post-graduate are synonyms.  This may seem contradictory (since you might expect post-graduate to refer to something after graduate) but that is how it's used.  I understand this as coming from the fact that a post-graduate degree is something that you work toward following your graduation (i.e. the moment when you earn your undergraduate degree).

My impression is that people within academia generally prefer the term graduate to post-graduate in both contexts; the word post-graduate is used more often by non-academics, to whom the word graduate is more likely to seem ambigiuous.  

So you could say you have an undergraduate degree and two graduate degrees.  You could also describe your degrees as post-graduate degrees for further clarification, which would normally be needed only when speaking to someone not intimately familiar with academia.