We present the relation between stellar specific angular momentum j ∗, stellar mass M ∗, and bulge-to-total light ratio β for The H i Nearby Galaxy Survey, the Calar Alto Legacy Integral Field Area Survey, and Romanowsky & Fall data sets, exploring the existence of a fundamental plane between these parameters, as first suggested by Obreschkow & Glazebrook. Our best-fit M ∗-j ∗ relation yields a slope of α = 1.03 ± 0.11 with a trivariate fit including β. When ignoring the effect of β, the exponent α = 0.56 ± 0.06 is consistent with α = 2/3 that is predicted for dark matter halos. There is a linear β-j ∗/M ∗ relation for β ≲ 0.4, exhibiting a general trend of increasing β with decreasing j ∗/M ∗. Galaxies with β α 0.4 have higher j ∗ than predicted by the relation. Pseudobulge galaxies have preferentially lower β for a given j ∗/M ∗ than galaxies that contain classical bulges. Pseudobulge galaxies follow a well-defined track in β-j ∗/M ∗ space, consistent with Obreschkow & Glazebrook, while galaxies with classical bulges do not. These results are consistent with the hypothesis that while growth in either bulge type is linked to a decrease in j ∗/M ∗, the mechanisms that build pseudobulges seem to be less efficient at increasing bulge mass per decrease in specific angular momentum than those that build classical bulges.