Christine Quinn claims her estranged husband never paid for hospital bills tied to their son's birth -- and now she's gunning for primary custody of the kid amid their ongoing divorce.

The "Selling Sunset" star just filed a response to Christian Dumontet's divorce petition from 2 weeks ago -- and she has some startling claims in her paperwork ... including the allegation that he never paid off a huge lingering medical tab from the birth of their son.

In the docs, obtained by TMZ, Christine claims these hospital bills ended up amounting to over $100,000 -- the total amount, she says, has yet to be determined -- and she alleges that Christian had assured her he would foot the bill and pay it off himself.

However, Christine claims he did the opposite, letting these bills fall into collections ... which she says happened under her name and seriously damaged her credit.

Christine claims Christian allowed this to happen without her knowledge -- and now she's asking for primary physical and legal custody of their boy. She's also requesting spousal support ... and asking the court to reject Christian's ability to get any alimony on his end.

In terms of shared property and assets ... she says that has to be determined -- but mentions this alleged hospital bill tale as a tidbit in laying out the estranged couple's debts and assets.

Christine has also filed an answer to Christian's domestic violence TRO against her -- remember, she filed one against him as well -- and she details stuff she already claimed against him in her own restraining order filing. There's a hearing on that set for Wednesday.