Second-harmonic generation (SHG) is investigated from three kinds of lithographically fabricated plasmonic systems: Al monomers, Au monomers and Au-Al heterodimers with nanogaps of 20 nm. Spectrally integrated SHG intensities and the linear optical responses are recorded and compared. The results show that for the monomer nanoantennas, the SHG signal depends sensitively on the linear excitation of the plasmon resonance by the fundamental wavelength. For Au-Al heterodimer nanoantennas, apart from fundamental resonant excitation, nonlinear optical factors such as SH driving fields and phase interferences need to be taken into account, which play significant roles at the excitation and scattering stages of SHG radiation. It is interesting to note that a possible energy transfer process could take place between the two constituting nanoparticles (NPs) in the Au-Al heterodimers. Excited at the linear plasmon resonance, the Au NP transfers the absorbed energy from the fundamental field to the nearby Al NP, which efficiently scatters SHG to the far-field, giving rise to an enhanced SHG intensity. The mechanisms reported here provide new approaches to boost the far-field SHG radiation by taking full advantage of strongly coupled plasmonic oscillations and the synergism from materials of different compositions.