You cannot sync calendars but you can share your calendar with your spouse. Here are the steps:
You can share a calendar with one or more people in iCloud. Those you invite receive an invitation to join the calendar.
- Go to the Calendar app
on your iPhone. - Tap
at the bottom of the screen. - Tap
next to the iCloud calendar you want to share. - Tap Add Person, then enter a name or email address, or tap
to browse your contacts. - Note: Your contacts must have an email address to share an iCloud calendar. See Add and use contact information.
- Tap
.
These instructions are copied from the link below. It offers more good information. You may want to read it. But please come back here is you have questions.
Share iCloud calendars on iPhone - Apple Support