We perform a systematic study on the interactions of the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$ systems within the framework of chiral effective field theory. We introduce the contact term, one-pion-exchange and two-pion-exchange contributions to describe the short-, long-, and intermediate-range interactions. The low energy constants of the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$ systems are estimated from the $N\overline{N}$ scattering data by introducing a quark level Lagrangian. With three solutions of LECs, all the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$ systems with isospin $I=1/2$ can form bound states, in which different inputs of LECs may lead to distinguishable mass spectra. In addition, we also investigate the interactions of the charmed-bottom ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{\overline{B}}^{(*)}$, ${\mathrm{\ensuremath{\Sigma}}}_{b}^{(*)}{D}^{(*)}$, and ${\mathrm{\ensuremath{\Sigma}}}_{b}^{(*)}{\overline{B}}^{(*)}$ systems. Among the obtained bound states, the bindings become deeper when the reduced masses of the corresponding systems are heavier.