Phpmyadmin / mysql error defining primary keys as foreign keys of two separate tables
Tried to create a database with the exact tables, PKs and FKs as yours and I receive no error. 
Tried both creating the tables with the constraints and without it, creating the relationships via PHPMyAdmin.

This "Error" you're getting really doesn't have a message or a error number?

To answer you, yes, you can set two columns as Primary Keys that are also Foreign Keys. They should look like this:

person_id_number 1 (referencing p.id_number 1)
email_addres_idnumber 1 (referencing e.id_number 1)


Now, as they are PKs, you can't repeat them. You could only use the Person ID 1 to another Email ID, and vice-versa. 

But, as you also have and ID number in your map, there will be some repetitions:

id_number 1
person_id_number 1
email_address_id_number 1


Looks ok, right? But:

id_number 1
person_id_number 1
email_address_id_number 2


Now you have two id_numbers, because your Primary Key consists of three different tables. What I'd suggest you is for you to create the PK as the id_number of the map table and the foreign keys as a Unique Key. It should look like PK(id_number), UK(person_id_number, email_address_id_number).