All you have to do is have the other person log on to the website AND the app (which they should then never log out of) with whatever email address and AirBnB password (should be kept different from your email password) the two of you agree to use. If you choose to use YOUR email address, you don't have to give the second person access to your email, but you'll continue to see whatever level of email interaction you've set at AirBnB. In general, the other person doesn't need to see or use emails related to the listing; everything can be handled with the site and apps' messaging system.
If you both stay logged in under your chosen email address, you will both receive "Push" notifications from the app if you set it to send Push notifications. You can also set it to send (or not send) standard SMS text messages to you, duplicating the Push notifications, but they will only be sent to one phone number. You can specify which number from within the AirBnb web site (and possiibly the app).
Keep in mind that both the Push messages and (if used) text messages sent to your phones will only show messages FROM guests and lookers or AirBnB. Neither phone will receive mesaages (by either method) that are sent by you or your proxy host TO the guests, etc. You can see those if you want by logging into AirBnB (web site or app) and reviewing the message conversation with any given guest, etc.
By the way, this is the way we run our listing. Dede owns the property and does all the laundry. Which she doesn't like. Not one bit. Co-host Steve, a friend and neighbor (which is clearly mentioned in our profile and in communications with guests) handles most day-to-day details. And cleans the toilet. Which he doesn't like. Not one bit.
