Can I sue on the Note and the Mortgage at the same time if separate parties signed the Note and Mortgage?

Foreclosure actions are initiated against the real property. You can foreclose on whomever is on the mortgage. Your suit for the default on the note (a debt collection lawsuit) is separate from the foreclosure lawsuit to reclaim the collateral.

You cannot sue someone for liability on a promissory note if they only signed the mortgage. You will be required to sue the individual who signed the mortgage if you want to foreclose against the property. It may be wise to have an attorney handle this, as mortgage foreclosures are very administratively exhaustive and actually require a fair amount of experience to execute properly. Good luck with your case!