The recent literature has emphasized the role of occupations in quantifying the amount of telework possible under social distancing measures during the COVID-19 outbreak. However, telework requires not only a teleworkable occupation but also household inputs related to basic infrastructure (Internet connection and other housing services) and time availability. We use a recent household survey that includes rich information for large urban areas in eleven Latin American countries and we find that these household inputs are not available for more vulnerable workers. This introduces additional sources of in- equality in the possibility of working from home, aside from those imposed by occupations, as well as it reinforces the association between economic development and the share of tele- workable jobs. We also analyze the profiles of workers in jobs that imply a higher exposure to the virus (high personal-proximity jobs), and we find important additional sources of inequality. In particular, workers in jobs of higher exposure to the COVID-19 also have other health risks, implying that this type of inequality should be carefully taken into account when designing deconfinement measures.