The chemical composition of planets is inherited from that of the protoplanetary disk at the time of planet formation. Increasing observational evidence suggests that planet formation occurs in less than 1 Myr. This motivates the need for spatially resolved spectral observations of Class I disks, as carried out by the ALMA chemical survey of Disk-Outflow sources in Taurus (ALMA-DOT). In the context of ALMA-DOT, we observe the edge-on disk around the Class I source IRAS 04302+2247 (the butterfly star) in the 1.3mm continuum and five molecular lines. We report the first tentative detection of methanol (CH$_3$OH) in a Class I disk and resolve, for the first time, the vertical structure of a disk with multiple molecular tracers. The bulk of the emission in the CO 2-1, CS 5-4, and o-H$_2$CO 3(1,2)-2(1,1) lines originates from the warm molecular layer, with the line intensity peaking at increasing disk heights, $z$, for increasing radial distances, $r$. Molecular emission is vertically stratified, with CO observed at larger disk heights (aperture $z/rsim0.41-0.45$) compared to both CS and H$_2$CO, which are nearly cospatial ($z/rsim0.21-0.28$). In the outer midplane, the line emission decreases due to molecular freeze-out onto dust grains (freeze-out layer) by a factor of >100 (CO) and 15 (CS). The H$_2$CO emission decreases by a factor of only about 2, which is possibly due to H$_2$CO formation on icy grains, followed by a nonthermal release into the gas phase. The inferred [CH$_3$OH]/[H$_2$CO] abundance ratio is 0.5-0.6, which is 1-2 orders of magnitude lower than for Class 0 hot corinos, and a factor ~2.5 lower than the only other value inferred for a protoplanetary disk (in TW Hya, 1.3-1.7). Additionally, it is at the lower edge but still consistent with the values in comets. This may indicate that some chemical reprocessing occurs in disks before the formation of planets and comets.