Custody Without Divorce

Location: NY
Hello everyone.
I’m looking for advice from people familiar with NY Family Court.
My husband and I are still married and technically together, but our relationship is in a very bad place. We still live together, travel together, and have intercourse.
We recently moved to NYC, and as I understand it, we need to live here for a year before we can file for divorce. Because we just moved, we can’t get divorced right now.
After I called the police following an incident between us, my husband got angry and filed for custody of our baby. We have a newborn.
In his custody case, he claims that I’m “crazy” and that he has safety concerns about me caring for our baby. He has also claimed to have safety concerns about his own life. However, we still live together, travel together, and have sex. He also trusts me to care for our baby for four days at a time. He wants 3 days with the child.
Important facts to mention: my husband is a social worker who works in a NYC family justice center. Despite the fact that he is a social worker he still verbally and emotionally abuses me at home.
Also my husband always brings up the fact that he is Black and I am white and people would rather believe me than him. But I myself have never thought of such a thing. He explains that the reason why he wants custody is to have legally obtained time he can spend with his child. He wants to be able to go to the park with our baby by himself not worrying that one day i will call police on him and say he kidnapped a baby, however I would never do such a thing.
I tried to talk to him but he is not someone who would sit and discuss things.
Could these inconsistencies raise questions about his claims in court? Would a judge consider the fact that he continues to live with me, travel with me, and leave our baby in my care despite claiming to have serious safety concerns? Or could the judge still believe his allegations?
Is it even possible to get physical custody and visitation while still living together?
I’d appreciate hearing from anyone who has experienced something similar or understands how NY Family Court handles custody cases when parents are still married, living together, and having serious relationship problems.