Can my spouse take the course with me?

Absolutely! You'll need to share the same account -- the email with which you enroll is used for all course communication. You're welcome to forward your significant other the daily lesson emails, or change your email address to a shared address. 

You can both participate in the forums under the same account, too. Some couples change their display name to reflect both of their names, and then sign off accordingly. =) 

Please be aware that course progress is account-wide, not device-specific. If you're taking the course together but on separate devices, and one of you marks a lesson as complete, then both of you will see that lesson as completed. You might need to pay extra attention to your individual course progress!