We have used multiphoton excitation via selected intermediate states to observe and identify triplet Rydberg series of the type msnp**3P**0 up to high n in Ca, Sr, and Ba. Previous efforts have failed to identify these series beyond n equals 7. We present details of our experimental method, give tables of the newly determined energy levels, and describe their analysis by multi-channel quantum defect theory (MQDT). For the most part, the msnp**3P**0 series in Ca and Sr can be described by a nearly constant quantum defect delta with delta //C//a equals 19. 7 and delta //S//r equals 2. 90. The 6snp**3P**0 series in Ba is more heavily affected by the configuration interaction, but to a reasonable approximation has delta //B//a approximately equals 3. 81. For all three elements, we find that the msnp **1P**0//1 series are much more strongly perturbed than the **3P**0//1 series. Most of this paper treats Ba. In addition to the **3P**0 states, **3F//2 and **1G//4 states are measured and tabulated. Further results in Ba include new and/or revised values for some **1P**0//1 states a revised ionization limit, evidence for an energy-dependent configuration interaction, and an MQDT prediction of the photoabsorption cross section at the ionization limit. This prediction agrees with the most recent experimental cross section. The MQDT analysis of Ba is described in great detail to make it useful as a guide to the reader who wishes to become a user of MQDT.