Can someone with AoE II: HD edition play multiplayer with someone who has AoE II: definitive edition?

My Friend on steam has the HD edition of AoE II but I have the definitive edition, is the multiplayer too different or is there a way we can play against each other?

No, you cannot play multiplayer against your friend. The versions are not compatible.

This Reddit post has explanation why:

Not possible for a simple reason. Definitive edition is server-based meaning that all commands executed by the players are handled by the server. On the other hand HD edition is peer-to-peer based so executed commands by players are shared with each other and when a player lags the rest of the players are affected by the lag.