To do so, use the unclass() function.
tab <- with(airquality, table(OzHi = Ozone > 80, Month, useNA = "ifany"))
class(tab)
## [1] "table"
unclass(tab)
## Month
## OzHi 5 6 7 8 9
## FALSE 25 9 20 19 27
## TRUE 1 0 6 7 2
## <NA> 5 21 5 5 1