What is the thesis of Jarhead?

There is not a single thesis for Jarhead.  That is because a thesis is an argumentative statement that another writer makes about the novel.  The thesis statement could be about characters in the novel or main themes present in the novel.  It is up to you.  

The novel is not exactly a glowing endorsement of the military or individual soldiers, so I would tailor your thesis in that direction.  Perhaps focus on Swoffie's disillusionment...

There is not a single thesis for Jarhead.  That is because a thesis is an argumentative statement that another writer makes about the novel.  The thesis statement could be about characters in the novel or main themes present in the novel.  It is up to you.  

The novel is not exactly a glowing endorsement of the military or individual soldiers, so I would tailor your thesis in that direction.  Perhaps focus on Swoffie's disillusionment that continues to grow throughout the novel.  He chose to be a Marine, but he struggles with knowing that the military has successfully turned him into that and nothing else.   

I hated being a marine because more than all of the things in the world I wanted to be—smart, famous, sexy, oversexed, drunk . . . — more than all of those things, I was a marine.

A thesis could be based on those feelings.  For example, "Although most readers might assume that many young soldiers are proud to call themselves marines, Jarhead shows readers that the title might actually be hated by many soldiers."  

The end of the book is a tough read, but the main message speaks out against thinking that American soldiers are all war heroes.  A thesis could be made with that thought in mind.  For example, "Many times war movies and novels portray the American soldier in a glorified, heroic light; however, Jarhead gives readers a much darker view of the American solider."