This Letter presents the first simultaneous measurement of the quasielasticlike neutrino-nucleus cross sections on C, water, Fe, Pb, and scintillator (hydrocarbon or CH) as a function of longitudinal and transverse muon momentum. The ratio of cross sections per nucleon between Pb and CH is always above unity and has a characteristic shape as a function of transverse muon momentum that evolves slowly as a function of longitudinal muon momentum. The ratio is constant versus longitudinal momentum within uncertainties above a longitudinal momentum of 4.5  GeV/c. The cross section ratios to CH for C, water, and Fe remain roughly constant with increasing longitudinal momentum, and the ratios between water or C to CH do not have any significant deviation from unity. Both the overall cross section level and the shape for Pb and Fe as a function of transverse muon momentum are not reproduced by current neutrino event generators. These measurements provide a direct test of nuclear effects in quasielasticlike interactions, which are major contributors to long-baseline neutrino oscillation data samples.