Making changes to email in members also change customer profile

I noticed recently that when a user edits their account profile using the members app template, it doesn't also change their email address in the customer profile. Is there a way to combine these so that the customer can adjust their details at the same time with one form? I realize that members is just used for authentication and linked to a customer profile, but it would make sense to allow them to change their information in both places. Is this already possible?