Can you help me ID this bird?

I think it was a kind of woodpecker or nuthatch. There were two, and I’m fairly certain they were a male and female pair. Both were a bit bigger than sparrows. The male had a black and white striped head and a red beak – the beak itself was red, no other red on him. His belly was solid gray and his back was spotted black and white. The female looked a lot like him but she had a brownish tone. I live in the northeast US. I don’t seen anything in my birdbook matching this description, but many birds are changing colors for the winter and I’m thinking maybe my book just shows summer coloring. Any ideas?