"together with both" is correct and usable in written English.
You can use it to refer to two things that are combined. For example, "We had a great time together with both our families."
They end up going to the movies together with both sets of friends".
The Duke and Duchess of Cambridge have released pictures from their first holiday together with both their children.
Mr. Sheldon said he found the movie therapeutic because it brought him together with both his colleagues and his feelings.
For the club and its trainer, the match marks the beginning of their last few months together – with both parties looking to end the relationship on a high.
"Would you like to swim with me in the Crazy Pool, Mr. Vainberg?" she asked, bunching her young buds together with both hands.
Put together, these two reports suggest a compromise is being strung together, with both the IMF and the ECB giving enough ground to get Greece's delayed aid tranche through.
He was never expecting a flurry of points from a fixture list that unkindly threw Bolton together with both Manchester clubs, Liverpool, Arsenal and Chelsea in their first seven matches.
Sida is now, together with both truck manufacturers Volvo and Scania, supporting vocational schools for mechanics in Ethiopia and are preparing to bring similar concepts to Liberia, Mozambique and DR Congo, together with other major Swedish and international manufacturing companies.
In Alexandria Greco-Roman Museumm) there is a mosaic (depicting Erotes fighting a stag and, in the outer border, a frieze of animals) in which cut, triangular tesserae are used together with both pebbles and lead wire.
Blessed and cursed with extraordinary lives, they're two very different, flawed heroes who only stop making mistakes and grow to their best when they arrive together (with both implicitly knowing that they might need to push certain buttons to get each other there).
Physics problem solving expertise was assessed by a common quiz given to students together with both homework assignments.
