Who was Toph's husband
The creators finally decided to name Lin Beifong's father.
Season 4, Episode 10: Operation Beifong :
(while Bolin, Opal, Toph and Lin are sitting by the fire for dinner)
Bolin: So, here's something I've always been curious about! Who's Lin's dad?
Toph: He was a guy named Kanto. Nice man, but it didn't really work out between us.
Bolin: Aaaaaaand... okay!
Aaaaannd.. That's it. Lin's dad is some guy named Kanto (Toph pronounced it Kahn-Toe). No more info (yet).
Toph has a second daughter, Suyin Beifong, half-sister of Lin, and we still don't know who Su's father is. Toph probably had multiple husbands/lovers. Let's wait for the writers to reveal more!
The official(?) Legend of Korra family tree (below) seen floating around the interwebs simply says "Unknown father" for Lin Beifong.
Speculation or reverse engineering of the facts we already know from both the series so far isn't sufficient to answer this question.
We will need to patiently await the creators for the answers to this one and more ('What happened to Zuko's mother?', 'Who is Amon?' etc.) through the show or through associated print media such as the comics and magazines based on the series.
Picture corrections (spoiler warning):
- Bumi developed Airbender abilities in the third season
- Toph Beifong has two daughters (Lin and Suyin Beifong)
- Bolin is an Earth bender and discovered in the third season he can Lava bend too.
I don't think it's Sokka. In Avatar: Legend of Korra, Lin was an ex-gf of Tenzin. If Sokka is Lin's father, then Lin is Tenzin's cousin. That makes absolutely no sense. I think Toph's husband is someone who is not introduced in The Last Airbender. :)