How to submit illustrated novels?

Hmm... This submission sounds uncouth but not impossible. You might have to wing it. I've not heard of unpublished authors submitting an MS with illustrations included.

Take my advice with a grain of salt. I really don't know and Google brought up nothing useful for me.

As you say, publishers usually assign illustrators to authors. Are you dead set on fulfilling both roles? If it was written by you and illustrated by someone else, would you feel like you hadn't met your goal? If so, look into self-publishing.

If not, treat the two separate issues as two separate issues. Get a publisher interested in your book, and then begin the discussion of your desire to self-illustrate. Try to remain satisfied even if all they buy is your writing.

A publisher (or agent who accepts author/illustrators) will have guidelines for this sort of situation. (I have just checked Arthur Levine's.) Since you are offering, first and foremost, an illustrated text, I would follow the guidelines for a novel but mention illustrations in the cover letter and, as they specify, either provide a link to an online portfolio with samples of the relevant illustrations or include (placed after the manuscript sample pages) printed copies of no more than three illustrations.

Don't try to embed the illustrations within the text unless they are genuinely integral to the written word (e.g., the Whimpy Kid series).

Edited to add: as the others said, ordinarily the publisher decided if a book will be illustrated and what artist will create them. Even many picture books start off as manuscripts of pure text by writers who will not (or even cannot!) illustrate them.