Enthalpy is not linked simply with bonds, nor does it consist of heat.
Enthalpy is an energy that
- Does not fully reside in the considered body, as opposed to internal energy;
- But can be fully computed from the state of the considered body;
- Is very useful to compute heat fluxes and work. Tables give H rather than U.
Consider the extreme case of a liquid, taken non-compressible for simplicity. As it flows from a high to a low pressure, its internal energy doesn't change, but it can acquire speed or rotate a turbine. The change of P*V, here V*ΔP, lets us calculate this energy amount that U doesn't incorporate.
V*ΔP does not come from the liquid amount that passes through the turbine. The higher upstream pressure is provided by the liquid upstream, that has not passed through the turbine. Though, we can measure the P just before and after the turbine, at the liquid amount that passes through the turbine.
As a generalization, H adds PV to U because a part of the work or of the heat flux comes from outside the considered body hence is not internal energy. Then it applies to gases too, and in fact to any body.
Sidenote: thermodynamics applies to gases and liquids usually and historically, but is more general. Depending on the topic, U, H and the others can incorporate electric, magnetic, nuclear... energy to make useful predictions, about superconductors or nuclear equilibrium in multi-million-Kelvin plasmas.