My girlfriend and I receive full coverage under a *family* HDHP from her employer.
Actually, no you don't. You're not legally married so you can't legally have a "family" plan of any type, in any way, shape or form unless you have a child or other dependent that you have legal custody of. The $3K is "in fact" income paid to you for nothing, and you are required by law to report it on your tax return. It won't be self-employment income. But it "is" reportable income that you must include on your tax return if it's your SSN in the "Recipient's TIN" box of that 1099-MISC.
