We studied the nuclear obscuration of galaxies hosting Low Ionization Narrow Emission Regions (LINERs) based on their X-ray and optical emission. X-ray data show that high obscuration is a common property of LINERs, 50% of them are identified as good candidates to be Compton-thick. From the Hα HST-imaging analysis it is found that the large majority of them exhibit an unresolved nuclear source surrounded by extended emission with irregular morphologies. The Hα morphologies are grouped into three classes: nuclear outflow candidates (42%), core-halo morphologies (25%), and nuclear spiral disks (14%). Only five out of the 36 LINERs are classified as dusty objects. A size-luminosity relation is found between a characteristic radius of the emitting nebulosity and the hard X-ray luminosity, favouring the AGN-NLR nature of the ionized gas in these LINERs. From this X-ray/optical analysis it came out that all dusty objects are Compton-thick and thus the material obscuring the putative AGN could be external to the NLR. For the other sources no clear relation is found between Compton-thickness and obscuration. Therefore the material responsible for the measured obscuration needs to be located in the very inner regions of the AGN.