This character is Henry's Italian surgeon roommate. Unfortunately, we have to start with the next information – Rinaldi is an alcoholic womanizer who does not believe in romance and love as Henry does. Instead, he proclaims himself in love with nearly every woman he meets, then quickly discards the idea as he finds the next one.
Basically, his character plays a crucial role in the text. He is described as a dominator on all male characters. He is kind, loyal, and good-natured.
Some period of time he was in love with Catherine, but after several attempts to start getting out somewhere with her, he understood that stuff like that isn’t for him. That is why he was seen in the whorehouses all over the town and further. Later, his best friend Henry finds out that the Lieutenant has syphilis and unfortunately he will end up very sad and unpleasant. Nevertheless, the author doesn’t cover this reality; he decides to make as real as he can. He wants us to know that each action has a reaction; that a person has to answer his/her actions sometime. And the disease Rinaldi gets seems to be completely merited.
What is more, if it was a woman with syphilis Hemingway would describe her as a complete failure of a "womanity" (like humanity, but just from the women’s side). It is one more score to the author’s hate to womankind.
Moreover, to the middle of the text, we see how he appears to have something of a crush on Henry, or at least engages in what literary criticism refers to as a "homosocial relationship," a bond between men that borders on homoeroticism.
Lieutenant Rinaldi in the Essays