  Let $X$ and $Y$ be compact Hausdorff spaces, $E$ and $F$ be real or complex
normed spaces and $A(X,E)$ be a subspace of $C(X,E)$. For a function $f\in
C(X,E)$, let $\coz(f)$ be the cozero set of $f$. A pair of additive maps $S,T:
A(X,E) \lo C(Y,F)$ is said to be jointly separating if $\coz(Tf)\cap
\coz(Sg)=\emptyset$ whenever $\coz(f)\cap \coz(g)= \emptyset$. In this paper,
first we give a partial description of additive jointly separating maps between
certain spaces of vector-valued continuous functions (including spaces of
vector-valued Lipschitz functions, absolutely continuous functions and
continuously differentiable functions). Then we apply the results to
characterize continuous ring homomorphisms between certain Banach algebras of
vector-valued continuous functions. In particular, the results provide some
generalizations of the recent results on unital homomorphisms between
vector-valued Lipschitz algebras, with a different approach.
