This show is very similar to Mission Impossible

Watching an MI ep recently involving a fictional eastern European dictatorship & noticed how the IM force infiltrate the rival nation by adopting phony accents and conning their way around various high officials.

(MI is a fun show but in many ways it is unintentionally funny to the modern viewer.)

MI & HH both involve elaborate and far-fetched schemes of trickery against the enemy, both have an ensemble cast. Both shows started almost the same year (1965/66), & IIRC both were filmed at Desilu.

Both also utilize very similar set pieces of 'espionage music' when the actors are doing various bits of spy business.

MI differs from HH in that most of the IM force don't show much of their personality, excepting maybe Martin Landau & Barbara Bain. The actors tend to emote when they are masquerading as foreign officials & agents, but otherwise they are mostly ciphers. (I think this was by design, the idea being that they were all highly professional, effectively submerging most of their own emotions, etc.)

HH of course derives much of the humor from the various personalities and the interplay.

Ivan Dixon usually got the least interesting jobs on HH, but compared to the lines Greg Morris got, Dixon's work on HH was positively Shakespearinan. (Despite not getting a lot of great lines on MI, Morris stayed with the show till it ended in 1973, so obviously it was a pretty good gig for him.)

Both MI & HH were among the earliest shows to feature black actors as regulars, with 'I Spy' featuring Bill Cosby also debuting in 1965 as well. ('Car 54 Where Are You' debuted in 1961, and the great Nipsey Russell was in 15 episodes, making him a semi-regular.)