Recent work has established large samples of astrometrically confirmed RR Lyrae and type-II Cepheid members of Galactic globular clusters (GCs). Any given GC can contain multiple such stars at once, notably RR Lyrae stars pulsating in the fundamental mode (RRab) or the first overtone (RRc), and type-II Cepheids (T2Cep) of BL Her and W Vir types. Here, we present the first joint calibration of the Leavitt laws (LL) exhibited by 802 RRab, 345 RRc, and 21 T2Cep stars anchored to trigonometric parallaxes. Using the third data release of the ESA Gaia mission (GDR3), we have calibrated the intercepts of the RRab and RRc Leavitt laws in the reddening-free Gaia Wesenheit magnitude, MWG, to better than 1.0% in distance, and that of T2Cep to 1.3%, using a global fit to all data. The absolute scale is set by 37 nearby GCs with high- accuracy parallaxes while 56 additional GCs provide constraints on LL slopes as well as the LL intercept differences of RRc and T2Cep relative to RRab stars. Our global fit yields homogeneous high-accuracy distances of 93 GCs that show no evidence of bias for Gaia parallaxes of distant GCs. Control of systematics was demonstrated by 30 alternative fit variants, notably involving different treatments of metallicity effects, as well as by Markov Chain Monte Carlo analysis. Our results suggest that photometric metallicities of RR Lyrae stars require further improvements while also exhibiting possible signs of intra-cluster chemical inhomogeneity. This work lays the foundation for exploiting RRab, RRc, and T2Cep stars as high-accuracy standard candles for near-field cosmology and the extragalactic distance scale.