We present a novel stereo imaging technique called dual-focus stereo imaging or DFSI. DFSI uses a pair of images captured from different viewpoints and at different foci, but with identical wide aperture size. Each image in an DFSI pair exhibits different defocus blur, and the two images form a defocused stereo pair. To model defocus blur, we introduce a defocus kernel map (DKM) that computes the size of the blur disk at each pixel. We derive a novel disparity defocus constraint for computing the DKM in DFSI, and integrate DKM estimation with disparity map estimation to simultaneously recover both maps. We show that the recovered DKMs provide useful guidance for segmenting the in-focus regions. We demonstrate using DFSI in a variety of imaging applications, including low-light imaging, automatic defocus matting, and multifocus photomontage.