Why are Remy Danton and Jackie Sharp keeping their relationship a secret?

Question

In House of Cards Remy Danton and Jackie sharp are in a secret relationship and

this fact is used to blackmail Remy in Season 4.

Why do they need to keep this a secret?

Answer 1

Initially it was a clear conflict of interests (as suggested in Napoleon's comment), because each of them was having access to information very valuable to the other.

Their relationship began as a sex-fueled manipulation tactic, each trying to extort something from the other for their own personal gain. In Remy's case, he was trying to dig up damning information on Frank from his hand-picked (and decidedly not next-in-line) Majority Whip for the opposition. In Jackie's case, she thought that by seducing Remy, she might discourage him from giving his Republican bosses ammo with which to attack the Democratic leadership.

(source)

Later they broke up, but when they got back together Jackie was already engaged (and then got married) to Alan Cooke and they had to be even more secretive with the relationship.

In episode 11 of the 4th season Remy clearly states that Jackie will lose her seat in Congress if their relationship becomes publicly known.