Service is good in most states if papers are delivered to your home to someone "of suitable age and discretion." Unless your boyfriend is under the age of 12 or has an obvious mental handicap, honey you got legally served!
Hope this perspective helps!
It would be very risky to ignore the papers and you would open yourself up to the possibility of having a judgment by default entered against you.
If your boyfriend does not live with you, you could potentially make the argument that you were not correctly served, as the AZ rules of civil procedure require that the summons and complaint be personally delivered to the person being sued or left at that person's house with some person of suitable age and discretion "then residing therein." If he doesn't live there, you could try that argument. That's a stronger argument in Arizona than it is in many other states because AZ Rules of Civil Procedure specify that only certain individuals qualify as to serve process. In many other states, any individual over the age of 18 can serve legal papers. For example, in my state of Minnesota, once your boyfriend handed you the papers (assuming he's over 18 years old), you would be served. In Arizona, because of AZ Rule of Civil Procedure 4(d), your boyfriend shouldn't qualify.
I think that's a risky argument to make, though. And at best, it just seems to delay the inevitable of having a judgment made against you. If you're at the point where you're running from creditors and trying to avoid lawsuits on grounds like insufficiency of process because a significant other was given the papers, you may want to consider bankruptcy.
I would not ignore the papers because they will say you were served and in four months you will discover there is a default judgment against you when they garnish your wages. leaving papers at your address with a responsible adult is usually good service.
Disclaimer: This answer does not constitute legal advice. I am admitted in the States of New York, New Jersey and Massachusetts only and make no attempt to opine on matters of law that are not relevant to those three States. This advice is based on general principles of law that may or may not relate to your specific situation. Facts and laws change and these possible changes will affect the advice provided here. Consult an attorney in your locale before you act on any of this advice. You should not rely on this advice alone and nothing in these communications creates an attorney client relationship.