So I remembered it erroneously. Today I checked it in-game, and you are right. Here is the sollution:
Talk to your companion, let him form a Company. Close the dialog screen and the Party menu.
Go to the Camp Menu. Choose the "Take An Action" option.
Choose the "Organize Battle Arrays" option. Choose the Company you want to assign troops to.
Click through one more option-window. You arrive in a Party-Menu:
Now, you can give troops to and take troops from the new company. The men will vanish from your party menu, but fight with you in battle.
Good Luck!