We present photometry of the transient associated with γ-burst (GRB) 030329 obtained with the Cerro Tololo Inter-American Observatory 1.3 meter telescope and the ANDICAM instrument, a dual optical/infrared imager. Without the need for light-curve interpolation to produce snapshot broadband spectra, we show that the transient spectrum remained statistically achromatic from day 2.7 to day 5.6, during a rebrightening episode. Associating the light in these early epochs with the GRB afterglow, we infer a modest level of extinction due to the host galaxy in the line of sight toward the GRB: A$_V$(host)=0.30+/-0.03 mag for β=-0.5 and A$_V$(host)<0.4 mag (3 σ) for any physically plausible value of β (with flux f$_ν$åisebo x-0.5ex łambda$^- beta$). We conclude that the spectral slope of the afterglow component was more than β=-0.8 between day 2.7 and 5.6 after the GRB, excluding the possibility that the synchrotron cooling break passed through the optical/IR bandpass over that period. Taking extinction into account, a decomposition of the light curve into an afterglow and supernova component requires the presence of a supernova (SN) similar to that of SN 1998bw, an afterglow that shows some evidence for a second break around day 8-10 and a fifth rebrightening event around day 15. Assuming a, SN 1988bw-like evolution and a contemporaneous GRB and SN event, the peak SN brightness was M$_V$=(-19.8+/-0.4)-5logh$_65$ mag.