The couple walked into the paddock hand-in-hand in Bahrain on Saturday in a show of public unity.
Horner was cleared on Wednesday after an internal investigation into his behaviour towards a female colleague.
On Friday, he again denied allegations of inappropriate behaviour after a series of messages were leaked.
An anonymous email with a link to messages purporting to involve Horner had been sent to Formula 1 personnel and media on Thursday.
Geri Horner, a member of pop group the Spice Girls, appeared with her husband, and they were later pictured kissing before the season opening race. Red Bull dominated on the track with champion Max Verstappen winning and team-mate Sergio Perez second.
BBC Sport’s chief F1 writer Andrew Benson said that although it was a pointed appearance with cameras present, is not uncommon for Geri to appear at a Grand Prix, and that she attends several races each year.
Speaking to media on the paddock, Christian Horner said: “It’s been very testing for my family but we are very strong as a family and our focus is on this race.
“It’s the start of the season, and the team have done an incredible job over the winter to be starting on pole position in the best place possible, so let’s see what we can do in the race.
“We are here to go racing and that is my job. So this is what we are focused on and this is what we are here to do.”
After the race, Horner added: “Look it’s been the best possible start to the season, very clinical race by the team and well executed. The perfect start.”
Thursday’s anonymous email, which included a link to a drive of messages, was sent to 149 people involved in the sport, mainly senior figures and permanently accredited media.
After the messages emerged, Horner said in a statement: “I won’t comment on anonymous speculation. But, to reiterate, I have always denied the allegations.”
F1 president Stefano Domenicali and Mohammed Ben Sulayem – president of the FIA, the sport’s governing body – met on Friday in Bahrain to discuss the matter.
On Thursday at the Bahrain Grand Prix, Mercedes team principal Toto Wolff and his McLaren counterpart Zak Brown called for more transparency from Red Bull on the investigation.
The messages have been brought to the attention of the FIA and it is discussing the matter with F1 management.
