Sharing Apple Ids

It's not clear to me precisely what you're asking. Are you asking how you can both get the same emails? If so, you each need to add that email account to your devices. Or, are you asking how you can both get the same iMessage? If so, no, you can't as you have different Apple IDs. In order to get the same iMessages, you would need to share an Apple ID which is generally a bad idea.

I don't know if this would work for sure but one of you could try signing into only those two services using the other account. (In a few places Apple does let you sign into specific features on a mobile device if you want to use a different account for that service.)

Sign into a different Apple ID for these services in Settings. Note this has to be the same ID for both. Go to Settings > Messages > Send & Receive, and make sure both your telephone number and Apple ID are input there and both show a checkmark. If you need more help, check out this link: Add or remove your phone number in Messages or FaceTime - Apple Support