EuCuP and EuCuAs are members of a family of materials with candidates for realizing magnetically tuned electronic topology. In this work, the magnetic phase transitions and magnetoelastic coupling of EuCuP and EuCuAs have been investigated. Around the Curie temperature, the thermal expansion coefficient and specific-heat capacity of EuCuP are found to have two closely spaced features, at approximately 30 and 31.3 K, which may indicate a cascading magnetic transition or perhaps an electronic transition closely coupled to the magnetic ordering. The zero-field magnetoelastic coupling appears to be stronger in EuCuP than in EuCuAs, and field-dependent measurements suggest this is due to the dominant ferromagnetic interaction in EuCuP as opposed to antiferromagnetic order in EuCuAs below TN=13.5K. Thermal expansion is anisotropic around TN in EuCuAs, with a maximum expansion along  occurring above TN prior to a stiffening of this c-axis component on cooling through TN; the expansion of the basal plane has a lambda-like peak centered slightly above TN. Matching these behaviors, the ac susceptibility data for EuCuAs suggest the presence of strong ferromagnetic correlations above TN in the vicinity where the c-axis expansion peaks. Both compounds possess similar electrical and thermoelectric transport behaviors, with short-range magnetic order likely playing an important role above TC or TN. Transport properties suggest these are predominantly hole doped due to intrinsic defects, and narrow-gap semiconducting or semimetallic behavior may be achievable if the underlying defects can be tuned.