Instead of grabbing the second sacrificed piece, Black plays a defensive system - but he plays it too defensively. Hanging on to material, instead of returning it at the right moment, can spell disaster, even (especially) against the Jerome Gambit.
jankrb (2055) - musirpha (1874)
Giuoco Piano Jerome Gambit tournament, 2013
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+
4...Kxf7 5.Nxe5+ Kf8
Experimental are 6.Nd3, from Wall,B - Tim93612, Chess.com 2010 (1-0, 36) and 6.0-0 from billwall - DeDrijver, Chess.com, 2012 (1-0, 20).
Instead, 6.Qh5 is the rowdy Banks Variation, from Banks,P - Rees,M, Halesowen v Lucas BS, 2003 (1-0, 45). It is interesting to compare this line with the Paulsen Variation, where Black has placed his King on e7, instead of f8, e.g. the recently-discussed jankrb - Red House, Giuoco Piano Jerome Gambit tournament, RedHotPawn, 2013.
As noted as recently as in the game jankrb - Red House, Giuoco Piano Jerome Gambit tournament, RedHotPawn, 2013, the preferred capture is 6...dxc6, preventing 7.d4. The Database has many examples.
A bit better was 7...Bb6 as in perrypawnpusher - hdig, blitz, FICS, 2007 (1-0, 17) and perrypawnpusher - mika76, GameKnot.com, 2008 (1-0, 17).
Certainly an improvment over 8.f4 of perrypawnpusher - badhorsey, blitz, FICS, 2011 (1-0, 26).
8...Ke8 9.0-0 d6 10.c4 Nf6 11.e5 dxe5 12.dxe5 Ng8
13.Rd1 Bd7 14.e6 Nf6 15.exd7+ Kf7 16.Qxc6 Bd6 17.c5 Be5 18.f4 Black resigned