I am sorry he is putting pressure on something you clearly don't feel comfortable doing yet.
My little girl had a number of heart defects meaning we were in NICU for 6 weeks from birth with her while she went through a couple of surgeries and recovery. I had to leave her overnight there - but with the best trained babysitters on the planet!
When we got home, I didn't feel comfortable leaving her for quite some time. Thankfully the COVID restrictions actually came in handy, my husband was probably ready to leave her overnight quicker than I was but as we weren't going anywhere we didn't need to argue about it!
We managed to get into a routine fairly quickly, and she started sleeping through the night at 6 months (probably could have done from 4mths but I was actually waking her to feed her in the night on advice from HV). She now very very rarely wakes up in the night.
By 10/11mths I felt ready to leave her at night - by which I mean; we take her to her grandparents, I get her ready to bed and put her down, then we go out with grandparents watching the monitor, and we are back at grandparents around 11-12pm, and I wake up with her.
She is now 16mths and I have only left her overnight once where I didn't put her to bed and wake up with her, as we went to London for our anniversary. I personally found it difficult, but I did manage a 10am lie in which my body clearly needed!
3 months old is still so little and you have been through so much with her. Once she has grown out of the tiny stage, you may feel more ready to leave her overnight, but you should go at the pace you feel comfortable with and he should respect that. Even though he is trying to do a nice thing for your birthday, it isn't nice if you are just going to spend it worrying!