Are you talking about bond enthalpy or enthalpy of a reaction?
If you are trying to describe the strength of a bond between two atoms, what you are physically describing is the difference in energy between the two atoms locked together at a specific distance (the bond length) and the same two atoms at infinite separation. Chemically, you could write this process as:
HCl(g)
H·(g) + Cl·(g)
or you could say that the H-Cl bond is homolytically cleaved to give a hydrogen radical and a chlorine radical. Then the strength of the bond is the energy given off by that reaction.
You could also be considering heterolytic bond cleavage, which would be represented as:
HCl(g)
H
+(g) + Cl
-(g)
The other reaction you drew:
HCl(g)
(1/2)H
2(g) + (1/2)Cl
2(g)
is actually concerned with the strengths of three different bonds. The H-Cl bond is broken and H-H and Cl-Cl bonds are formed. The energy of the reaction in this case doesn't represent just the strength of the HCl bond, but the comparative strengths of HCl, H-H, and Cl-Cl bonds.