We present a deep Hubble Space Telescope (HST) imaging study of two dwarf galaxies in the halos of Local Volume Large Magellanic Cloud (LMC) analogs. These dwarfs were discovered as part of our Subaru+Hyper Suprime-Cam MADCASH survey: MADCASH-1 is a satellite of NGC 2403 (D~3.2Mpc), and MADCASH-2 is a previously unknown dwarf galaxy near NGC 4214 (D~3Mpc). Our HST data reach >3.5mag below the tip of the red giant branch (TRGB) of each dwarf, allowing us to derive their structural parameters and assess their stellar populations. We measure TRGB distances (D_MADCASH-1_=3.41_-0.23_^+0.24^Mpc, D_MADCASH-2_=3.00_-0.15_^+0.13^Mpc), and confirm the dwarfs' associations with their host galaxies. MADCASH-1 is a predominantly old, metal-poor stellar system (age ~13.5Gyr, [M/H]~-2.0), similar to many Local Group dwarfs. Modelling of MADCASH-2's color-magnitude diagram suggests that it contains mostly ancient, metal-poor stars (age ~13.5Gyr, [M/H]~-2.0), but that ~10% of its stellar mass was formed 1.1-1.5Gyr ago and ~1% was formed 400-500 Myr ago. Given its recent star formation, we search MADCASH-2 for neutral hydrogen using the Green Bank Telescope, but find no emission and estimate an upper limit on the HI mass of <4.8x10^4^M_{sun}_. These are the faintest dwarf satellites known around host galaxies of LMC mass outside the Local Group (M_V,MADCASH-1_=-7.81+/-0.18, M_V,MADCASH-2_=-9.15+/-0.12), and one of them shows signs of recent environmental quenching by its host. Once the MADCASH survey for faint dwarf satellites is complete, our census will enable us to test predictions from cold dark matter models for hierarchical structure formation and discover the physical mechanisms by which low-mass hosts influence the evolution of their satellites.