Aims. The aim of this paper is to study deuterated water in the solar-type protostars NGC1333 IRAS4A and IRAS4B, to compare their HDO abundance distribution with other star-forming regions, and to constrain their HDO/H2O ratios. Methods. Using the Herschel/HIFI instrument as well as ground-based telescopes, we observed several HDO lines covering a large excitation range (Eup/k=22-168 K) towards these protostars and an outflow position. Non-LTE radiative transfer codes were then used to determine the HDO abundance profiles in these sources. Results. The HDO fundamental line profiles show a very broad component, tracing the molecular outflows, in addition to a narrower emission component and a narrow absorbing component. In the protostellar envelope of NGC1333 IRAS4A, the HDO inner (T>100 K) and outer (T<100 K) abundances with respect to H2 are estimated at 7.5x10^{-9} and 1.2x10^{-11}, respectively, whereas, in NGC1333 IRAS4B, they are 1.0x10^{-8} and 1.2x10^{-10}, respectively. Similarly to the low-mass protostar IRAS16293-2422, an absorbing outer layer with an enhanced abundance of deuterated water is required to reproduce the absorbing components seen in the fundamental lines at 465 and 894 GHz in both sources. This water-rich layer is probably extended enough to encompass the two sources as well as parts of the outflows. In the outflows emanating from NGC1333 IRAS4A, the HDO column density is estimated at about (2-4)x10^{13} cm^{-2}, leading to an abundance of about (0.7-1.9)x10^{-9}. An HDO/H2O ratio between 7x10^{-4} and 9x10^{-2} is derived in the outflows. In the warm inner regions of these two sources, we estimate the HDO/H2O ratios at about 1x10^{-4}-4x10^{-3}. This ratio seems higher (a few %) in the cold envelope of IRAS4A, whose possible origin is discussed in relation to formation processes of HDO and H2O.
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