Films that start by announcing that they’re “inspired by a true story” don’t always live up to that claim. But there’s a sense of lived-in verisimilitude in “Thank You for Your Service” that makes this fact-based account of Army veterans crawling back to disappointing civilian life after combat tours in Iraq feel honest and genuine.

Solidly written and directed by Jason Hall (who provided the screenplay for Clint Eastwood’s similar biographical war film “American Sniper”), it earns our trust and doesn’t betray it afterward.

It’s an intelligent, solidly acted showcase for Miles Teller, who hasn’t lived up to the hopes inspired by his star-is-born breakthrough roles in 2013’s “The Spectacular Now” and 2014’s “Whiplash.” He plays Adam Schumann, who is fighting an ongoing mental war from his time in the Mideast.

As the bomb expert of his squad, he carried a sense of responsibility for everyone’s safety. When that crushing obligation beat down his ideals, he returned to Kansas in 2008 with physical and psychological traumas, including survivor’s guilt.

Sometimes his eyes show that he’s still back in action. But he employs the classic defense strategy with his supportive wife Saskia (Haley Bennett), keeping a tight lid on what’s wrong and acting like he’s just fine. “I can take anything you can,” she says. “Anything but quiet.”

He can’t find a job other than his teenage position tending a golf course. The local Department of Veterans Affairs offices, underfunded and short staffed, are required to process his pressing needs for benefits through a maze of rules he can scarcely tolerate.

Teller skillfully balances Schumann’s clashing currents of strength and self-doubt. Even more troubled are his comrades.

Will Wall (Joe Cole) returns angry and forlorn with a personal life that ignores his vulnerable state of mind.

Solo (Beulah Koale) bounces back to a warm relationship with his pregnant wife Alea (“Whale Rider” star Keisha Castle-Hughes). But he fights a losing tug of war with his battle-scarred memory — he can recall that he takes Klonopin to treat his panic disorders, but not what day of the week it is.

There’s little combat shown in this war film. The biggest struggles these men and their families face is their effort to come to terms with how scarred service has left them. The story is populated with characters who are hard to pin down to any fixed position on the spectrum between hero and heel. Their identities shift depending on who they’re dealing with, what the issues are, and what kind of a day they’re having. And don’t be misled by seeing Amy Schumer’s name in the credits. She effectively handles a surprising dramatic role presented in a way that never showcases her as a visiting celebrity cast against type.

The film’s title repeats the common salute to veterans and people in active duty, which can be sincere and heartfelt but often sounds as hollow as a politically correct gesundheit. It usually comes from people who have never worn a uniform, and it shows a lack of comprehension that is this film’s essential theme.

That being said, “Thank You for Your Service” is not a downer. It moves toward a hopeful finish that offers, if not a saccharine happy ending, at least some encouraging small victories.