The ANCOVA is equivalent to a multple linear regression.
In such a regression, you can include categorical and continuous
variables (and their interactions, if necessary). Likewise, in
ANCOVA you can include both types of variables as predictors.
The dependent variable in ANCOVA or in linear regression must
be interval scaled. If it is not, then ordinal logistic regression or
binary logistic regression or multinomial logistic regression
could be considered.