Yes, your relationship changes tremendously. How it's different very much depends on where you are in terms of parenting. I found it was different in specific ways earlier on, but that changed as my dd got older (it's still very different from before, not 'worse' but it's different in different ways as some things become a bit more like they used to be, if that makes sense). In the early weeks and months, everything is very intense and overwhelming. It's emotionally intense, draining, exhausting, and I definitely found myself very touched out. I was always holding, caring for, thinking about this baby, and there was little space and energy for much else. When I did have some rare downtime, the last thing I wanted to do was have a conversation with my husband, cuddle with him, show affection to anyone else. I was on empty. I'm not sure either of us really had a conversation about anything other than our daughter for about 6 weeks. If we weren't doing something with her, I don't think either of us could muster the energy to do anything but stare at our phones, stare at the tv or sleep. It's really, really hard.
I would think of this as like a hurricane. You're in the eye of it now. You may not be able to have date nights and cuddle and talk about life like you did before. You just need to keep your heads down, be kind to each other, give each other time to re-charge however you need to, and weather the storm until you pop out on the other side of it. You aren't 'just parents' now and the closeness is still there. But it goes on the backburner for a bit. My dd is nearly 5 now. The first 11 months or so were tough, not as tough as the first 8 weeks, but things did get easier little by little and we had more time and energy for each other again. I would say we are closer now than we ever were, but we still have less energy and we probably actually talk less in terms of deep conversations because you're just so done by the end of the day and you need to sit down and de-compress and zone out a bit. But our actual emotional connection and love for each other is stronger than ever. But go easy on yourself and him. It will get easier, but it just takes time to get on your feet again.