Bode Miller to Baby Mama -- I May Have a Yacht ... BUT I'M NO DRUNK

Olympic skiing champ Bode Miller is firing back at his baby mama ... claiming she's lying when she says he's bad dad material with a drinking problem.

TMZ broke the story ... Bode's baby mama Sara McKenna filed legal docs demanding primary custody of their newborn son ... claiming Bode's a drunk and an unsuitable father who lives recklessly on a yacht in San Diego.

She also said Bode didn't even want the kid and asked her to abort it.

Bode's lawyer tells TMZ ... the skier does NOT have a drinking problem and has wanted to be a part of the child's life ever since he found out he was the father. It's true ... Bode filed a paternity lawsuit earlier this year, asking for JOINT legal and physical custody.

As for his fathering skills -- Bode's lawyer says the skier's been a great dad to his other child ... and wants nothing more than to be a good one for his new son.

The lawyer says, "He is going to support his son. He wants to be part of the child's life."