Talk about why you're pumping. This is also very helpful, when a mom decides to exclusively pump because you will run into questions and comments from others like... Are you breastfeeding? Breastfeeding is so much easier, Pumping is SO much more work etc, why don't you just use formula? Decide how you want to respond to these questions in advance, remember its up to you to decide what you want to reveal. Some moms simply answer "my baby gets breast milk" while others choose to provide in-depth explanations of why they chose to pump and the importance of breast milk. It's important to let your spouse know your feelings and responses to this question in case they encounter them and so they can show support when they're with you and you're asked questions.
Tell your spouse how he can be helpful and make pumping easier for you - taking night time feedings, washing pump parts, etc. Many spouses want to be supportive or helpful but don't know how.
The most important part is to communicate! With a new baby, less sleep, and plenty of changes happening in your house this is no time to assume your spouse has mind-reading capabilities.