DH and I speak quite a lot, which looking at this thread is unusual!
We message back and forth throughout the day, things we've seen or random updates (today's: "Ooh just had that meeting with X finally" "Furious with the bank about this card mix-up, I just went in and they said Y") - it's mostly memes and nonsense, though.
It's not every day - if we're busy, we don't. But I work for myself and he has weird working times, so there are about an equal number of days where we do and don't message throughout the day.
And then we also call relatively regularly - a few times a week one will call the other at lunchtime to say hi, or we'll call while we're out and about and ask what the other fancies picking up for tea, or one of us is driving somewhere and just ring for a chat. He always calls on the way home from work, partly to ask if we need anything and partly just cos... we like talking to each other?
Reading the other replies makes mine sound like we're dangerously co-dependent, haha, but we're not. In the evenings at home we spend loads of time in our respective office/workspaces doing our own thing, spend plenty of time apart etc. But we just really like to chat to one another, and we're both talkers generally to think things through - we often talk each other through challenges or problems at work, or whatever.
Funny, as I know lots of people who message literally back and forth all day with SOs or call often, despite it being unusual in this thread - mostly under 35, though, so wonder if it's a 'having grown up with MSN and BBM and Whatsapp' thing. So I've never really considered it out of the ordinary!
Very different if you're trying to concentrate, though, OP - neither DH nor I would be remotely bothered if the other didn't answer a call/send a message back, and if the other had expressly said "No please don't call in the day", we wouldn't. So while I don't think his style/frequency of communication is that unusual or bad, the fact that you don't like it and he's doing it anyway is.