The phrase "a jacket with the" is correct and usable in written English.
It can be used when describing a specific type of jacket that has a particular feature or detail associated with it.
Example: "I found a jacket with the hood that I had been looking for all winter."
Alternatives: "a jacket featuring the" or "a jacket that has the".
He was wearing a jacket with the hood up.
Masha's lover, the macho Colonel Vershinin (Willem Dafoe), wears a jacket with the back rolled up like a window shade.
Joel Hyatt, the chief executive of Current, appeared in a jacket with the network's logo at a vigil for them in San Francisco this month.
The president was given a jacket with the letters NYPD emblazoned on the back and Potus (president of the United States) on the front, along with a seal of the police commissioner's office.
"I want to be closer to home right now and this is the closest we can get," said Laura Esposito, 34, of Boston, who wore a jacket with the Stars and Stripes pattern.
He performed "Crayon" early in the night, wearing a jacket with the head of a white tiger attached to the back, a pair of black Air Yeezy 2s and bleached blond hair standing straight up like sheaves of pesticide-soaked wheat.
You make a dress with a coat for the society look or a jacket with pants for the career look.
The day he went missing, 16-year-old Anthony Barnes Jr. was wearing a jacket with fur around the hood.
One man who appeared to be a supporter wore a jacket with an image of the drug kingpin Tony Montana from the movie "Scarface" on the back.
Frank Conroy's The Disinherited (Covici, Friede, 1933) appeared in a jacket with an illustration on the front and another jacket with blurbs by Whit Burnett and Erskine Caldwell, among others.
A jacket with cape sleeves, although revealing the breasts on the runway, would look chic in the conference room in the real world.
