Features of screening and confinement are studied for a non-Abelian gauge theory with a mixture of pseudoscalar and scalar couplings, in the case where a constant chromoelectric, or chromomagnetic, strength expectation value is present. Our discussion is carried out using the gauge-invariant but path-dependent variables formalism. We explicitly show that the static potential profile is the sum of a Yukawa and a linear potential, leading to the confinement of static probe charges. Interestingly, similar results have been obtained in the context of gluodynamics in curved spacetime. For only pseudoscalar coupling, the results are radically different.