Mexico called off its search for a cruise-ship passenger believed to have fallen into the Gulf of Mexico on Christmas night as her family said she may have taken her own life.

The Mexican Navy called off its search late Monday for Jennifer Ellis Seitz, a Florida journalist, who was reported missing by her husband about eight hours after a surveillance camera captured a person falling overboard. The U.S. Coast Guard had called off its search earlier in the day.

An FBI spokesman said Tuesday that agents were still investigating. No one has been charged.

Her husband, Raymond Seitz, was arrested earlier this year on a domestic battery charge, after he allegedly head-butted his wife. The charge was later dismissed after he completed a diversionary program. Records show that she asked the prosecutor not to pursue the case.

Seitz had "previous emotional issues," yet there were no outward signs of distress while on the seven-night cruise from Miami, her family said in a statement. Seitz's mother joined her daughter and son-in-law on the Norwegian Pearl, as the couple cruised to celebrate their first anniversary.

"Jennifer was in a very happy and uplifted mood both before and during the cruise," the Ellis family said in the statement. "She was excited about starting a new job and her future career with a local newspaper. She and her husband had been talking about starting their family. The family suspects that Jennifer chose an unfortunate ending to her life. She was a beautiful and caring person and will be truly missed by all who love her."

FBI spokesman Mike Leverock said agents were "still trying to determine if a crime occurred" after collecting evidence when the ship docked Sunday in Miami.

Norwegian Cruise Line said it is "cooperating fully" with the FBI.

"Our thoughts and prayers are with the family and friends of the guest during this difficult time," the company said in a news release.

Raymond Seitz has not been charged with any crime, authorities said Monday. A message left seeking comment at the couple's house wasn't immediately returned, and a call to the paving company that employs him rang unanswered.

The couple met in a weight loss support group; both had undergone bariatric surgery. She chronicled her weight loss journey for an Orlando TV station.

She was also a freelance writer, having written articles for The Tampa Tribune, The Ledger in Lakeland, and an online article titled, "Battling the Bulge Onboard," about how not to gain weight while aboard a ship.

On her Web site, Seitz described herself as an "avid traveler and an amateur chef." She was previously a reporter for Florida Today, a newspaper in Melbourne.

A fellow passenger on the ship, Jim Nestor, told NBC's Today show that Seitz and her new husband stood out on the ship with "large and raw personalities."

Many of the passengers saw them as contestants on an on-board game called "The Not-So-Newlywed Game," modeled after a 1960s TV quiz show. The game was also carried on the ship's closed-circuit TV channel.

"They stood out a lot more than other people," Nestor, a retired police officer, told NBC.

Nestor, who appeared on the game show with his own wife, said he ran into Raymond Seitz a day after his wife was reported missing.

"I had given him my condolences, and he had a plastic bag filled with quarters, and he said to me that he was going to the casino to see if he could change his luck," Nestor said.

The Associated Press contributed to this report.