From http://www.straightdope.com/columns/read/30/why-do-folks-say-jesus-h-christ
IHS would in fact look like IHC in some Greek scripts, as in Byzantine Greek, where sigma is written C. Whether that’s the answer, I don’t know.
See my post on the other thread on this topic. There are many examples of the IHC symbol for Jesus’ name in churches and other religious works of art. I have little doubt that this is where it derives from.
The Christogram (or logo of Christ’s name) IHC is an alternative for IHS, and is often found in old churches in the UK.
It is a transliteration of the Greek iota-eta-sigma, with the sigma represented by a C rather than an S.
See the following examples:Oxford,Trinity College, Dining Hall Orchardleigh, St Mary Earlham Cemetery, Norwich, Norfolk Guy’s Chapel Bury St Edmunds, Suffolk Byz./Medieval Lady’s Christogram Silver ring on eBay Cross at Grace Cathedral Church dedication: St Mary The Virgin, Long Stratton, Norfolk Church dedication: St Peter & St Paul, Lavenham, Suffolk Church dedication: St Mary the Virgin, Burston, Norfolk
There are probably thousands of examples in English churches.
It’s very easy to see that this could be taken as standing for Jesus H. Christ.