Total energies and various bound-state properties are determined for the ground states in all six four-body muonic ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ quasiatoms. These quasiatoms contain two nuclei of the hydrogen isotopes ${p}^{+},{d}^{+},{t}^{+}$, one negatively charged muon ${\ensuremath{\mu}}^{\ensuremath{-}}$, and one electron ${e}^{\ensuremath{-}}$. In general, each of the four-body muonic ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ quasiatoms, where $(a,b)=(p,d,t)$, can be considered as the regular one-electron (hydrogen) atom with the complex nucleus ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ that has a finite number of bound states. Furthermore, all properties of such quasinuclei ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ are determined from highly accurate computations performed for the three-body muonic ions ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ with the use of pure Coulomb interaction potentials between particles. It is shown that the bound-state spectra of such quasiatoms are similar to the spectrum of the regular hydrogen atom, but there are a few important differences. Such differences can be used in future experiments to improve the overall accuracy of current evaluations of various properties of hydrogenlike systems, including the lowest-order relativistic and quantum electrodynamics corrections to the total energies.