Yes, Catherine and Henry love each other; very much so, in fact. Throughout the course of their relationship, the pair defies the people and circumstances around them in order to be together. The relationship starts off with a twinge of tragedy; Catherine is mourning her lost fiance, killed during the Somme Offensive, and Henry is just looking to fool around. After Henry injures his leg in battle and he is sent to a hospital in Milan, Catherine is sent to the same hospital. The duo restart their connection, with the support of many of the other other nurses on duty at the hospital, including Misses Gage, Ferguson, and Walker. This happy time is not meant to last; Henry is sent back to the front. When he finds that he cannot stomach the war any longer and deserts, he manages to find his way back to Catherine. The pair end up leaving Italy altogether, canoeing to Switzerland. There, up until Catherine goes into labor, the young couple is very happy, and very in love.
They are, however, ultimately in an unhealthy relationship. Henry and Catherine become so wrapped up in one another that it’s hard to tell where one ends and the other begins. Catherine in particular seems to lose herself; she loves the idea of love, and is willing to smooth over her unique personality in order to keep her man - again, she says there is no her without him, no “separate” Catherine.
Cited: Hemingway, Ernest. A Farewell to Arms. New York: Scribner Classics, 1997. Print.