Nope. Self Harm in and of itself isn't normal. Common? Yes. Much like alcohol abuse & eating disorders are common. But neither normal, nor the expected consequence of being in a relationship (whether the person has PTSD or not). It's not like, oh! Of course you're binging and purging if you're dating someone with PTSD. Or, of course you're cutting yourself, abusing alcohol, etc. if you're dating someone with PTSD.
My question would really be is the SH something that's you ; ie how you respond to stress regardless of where it's coming from (like an eating disorder, or anything else that you'll be bringing into every relationship that you're a part of, regardless of how healthy/unhealthy the relationship is); or if it's something that has developed specifically in response to this relationship. There will always be a "you" (me) component in whatever your coping mechanism of choice is, but whether or not this is something that is just a part of your life and something you'll need to learn to manage, or whether this is where you go when under extreme duress? Would be really important to know.