In Catch-22, what is the balance of power between Yossarian and the chaplain?

Catch-22 opens with Yossarian’s reaction to meeting the chaplain:

It was love at first sight.

The first time Yossarian saw the chaplain he fell madly in love with him.

One might imagine that, due to the chaplain's status as a religious man and Yossarian's lovestruck state of mind, the balance of power would favor the chaplain. But contrary to the expectation of love at first sight, Yossarian describes his first impression as such:

Yossarian had no idea who he was and just took it for granted that he was either another doctor or another madman.

When under the impression that the chaplain is merely another officer, Yossarian is dismissive; however, upon realizing that the captain was also a chaplain, he is "astonished" and ecstatic. He is described as “[glowing] with affection” toward the chaplain, and calls him “sweet” after the chaplain had left. Perhaps the most telling line is this:

Yossarian wanted to help him.

In the first chapter, the balance of power clearly favors Yossarian. Although Captain Tappman is of equal rank and a chaplain as well, Yossarian feels himself superior to the chaplain and attempts to help him. Just as tellingly, the chaplain is described as flushing and blushing frequently throughout the encounter. His innocence is prominent: he "beamed gratefully" after Yossarian said he could visit him in the hospital.

Later in the book, the chaplain finds himself under Yossarian's protection. He sits with Yossarian and Dunbar at the officers club and feels safe, which he does not when alone. When Colonel Cathcart tries to throw him out, Yossarian "[rises] truculently to intervene" to throw an "avenging punch." 

As he is "sincerely a very helpful person who was never able to help anyone," the chaplain finds himself torn. He wants nothing more than to live quietly and return to his family, but he feels a sense of obligation to Yossarian. His attempt to talk to Major Major about the escalating number of missions fails; he believes himself to be the butt of a practical joke and with a "pleading whimper" escapes out the window. Particularly in comparison to Yossarian, who is, paradoxically, a brave coward, the chaplain appears far less resolved even as he attempts to aid him.

For all of his trepidation, the chaplain steps up when it is called for. Under suspicion of censoring letters under the name of Washington Irving, he recognizes Yossarian's handwriting and nonetheless refuses to give up his friend. After being punished for infractions he had never committed and accused of ridiculous crime, he is found guilty and told not the leave the island; in a "temper of scalding and vindictive resentment," he resolves to push the matter of the ever-growing number of missions. Though his attempt fails, it is growth regardless: the balance of power shifts in the chapter when the chaplain takes the fall for Yossarian and pushes for what is right.

In the hospital, the chaplain and Yossarian converse more as equals. The chaplain still blushes awkwardly, but Yossarian appears to value his opinion even though the chaplain didn't influence his decision: he had already planned not to take Cathcart and Korn's deal.

In the end, it is the chaplain's news that Orr has been washed ashore in Sweden that gives Yossarian the final push to leave. Yossarian, recognizing that Orr set up his escape deliberately, is jubilant; he calls on the chaplain to "for once in your life, succeed at something" and get him his uniform so that he can escape. Bolstered by Yossarian's confidence, the chaplain resolves to persevere in the face of Cathcart and Korn.

The power imbalance between Yossarian and the chaplain never reverses—Yossarian holds more sway throughout the relationship—but they both ultimately benefit from their friendship. While the chaplain is rarely able to aid Yossarian despite his dearest wishes to do so, he ultimately provides the catalyst for his escape; in turn, Yossarian gives him the gift of perseverance.