We present Hubble Space Telescope (HST) photometry of the late-type dwarf galaxy NGC 1705 observed with the Wide-Field Planetary Camera 2 (WFPC2) in the F380W and F439W bands and with the Advanced Camera for Surveys/High-Resolution Channel (HRC) in the F330W, F555W, and F814W broad-band filters. We cross-correlate these data with previous ones acquired with the WFPC2 in the F555W, F814W bands, and derive multiband color-magnitude diagrams (CMDs) of the cross-identified individual stars and candidate star clusters. For the central regions of the galaxy, where HST-NICMOS F110W and F160W photometry is also available, we present U, B, V, I, J, H CMDs of the 256 objects with magnitudes measured in all bands. While our previous study based on F555W, F814W, F110W, and F160W data allowed us to trace the star formation history of NGC 1705 back to a Hubble time, the new data provide a better insight on its recent evolution. With the method of the synthetic CMDs, we confirm the presence of two strong bursts of star formation (SF). The older of the two bursts (B1) occurred between ~10 and 15 Myr ago, coeval to the age of the central super star cluster (SSC). The younger burst (B2) started ~3 Myr ago, and it is still active. The stellar mass produced by B2 amounts to ~106 M sun, and it is a factor of ~3 lower for B1. The interburst phase was likely characterized by a much lower level of SF rather than by its complete cessation. The two bursts show distinct spatial distributions: while B1 is centrally concentrated, B2 is more diffused, and presents ring and arclike structures that remind of an expanding shell. This suggests a feedback mechanism, in which the expanding superbubble observed in NGC 1705, likely generated by the 10-15 Myr burst, triggered the current strong SF activity. The excellent spatial resolution of the HRC allowed us to reliably identify 12 star clusters (plus the SSC) in the central ~26'' × 29'' region of NGC 1705, 10 of which have photometry in all the UBVIJH bands. The comparison of the cluster photometry with the GALEV populations synthesis models provides ages from ≈10 Myr to ≈1 Gyr, and masses between ≈104 and 105 M sun. The conspicuous cluster population in the central regions, with one SSC, one populous cluster, and several regular ones, confirm the strong star-forming activity of NGC 1705. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA for NASA under contract NAS5-26555.