So yeah, I came up with this idea.
At the end of HL2 E2, Eli and Dr Kleiner mention the Borealis : Aperture science's (doesn't it remind you something ?) research ship which was found by Judith. You are about to go there with Alyx. I'll find a video.
Also :
I came by this while escaping in Portal 1 a minute ago.
Also, there are a lot of similarities : HEPs and Fusion Cores are the same thing, Aperture and Combine logos look close to each other, turrets, SFX, the final song also mentions Black Mesa.
=> One thing is clear : both stories are linked. Is HL2 E3 the bridge ?