Yes, it is possible to bet on both teams involved in a match at Bet365. This is known as "hedging" a bet. It allows you to place bets on both teams, effectively reducing your risk and potentially earning a profit regardless of the outcome of the match.
Like Betway, Bet365 sponsors multiple teams, including Leeds United, Newcastle United, and Wolverhampton Wanderers. Bet365 is one of the most prolific sponsors in the football world.