You said: The above statement seems to confirm that mind doesn't have occurrence without material body, and vise versa. Both factors are interdependent and seemingly co-exist.
Correct. In my (personal) understanding of Buddhist teaching, speaking in modern terms, Mind is Information. Information needs Media to carry it. And Media is Energy that takes certain Form due to the shaping influence of Causes and Conditions carrying Information. So Energy, Matter, and Information are aspects of the same underlying "ground of all".
"But, once, I heard that one's mind does't end at death of material body: how can that match with the above statement"?
In my (personal) understanding of Buddhist teaching, there is no such thing as "one's mind" - it's a mistake to think that way. Mind is not an entity, it's an aspect. Mind is like wind that goes in and out, like breath. Mind is information that is all around us, moving like wind.
I know this sounds like Materialism but it's not. With this interpretation we are not declaring the primacy of Matter. What I am saying is that "regular" Information and Energy is what the ancients called "spirit". This is what animates Matter. As a matter of fact, Matter, if you look at it very closely (at the level of electrons), is empty. It is only a shape that Energy takes.
This may also sound like Pantheism, as in, we are declaring that Mind is a global aspect of everything and that it is God. To this I respond that sure Mind is a global aspect of everything - but so is Energy, so is Space/Time - but we do not pray to Space/Time and declare it our God? Why should we identify Mind as God?
This may also sound like Nondualism, as in "I am this global Mind, and this global Mind is speaking through me now" and "The highest realization is to awake to unity with this global Mind" - but that would be conceit and self-identification, wouldn't it? Instead, as Buddha taught, the highest realization is to be free from conceit, free from such thoughts, and free from self-identification.
My Zen Master said: "operate mind, don't let mind operate you" and "you bless god, not 'god bless you'". This means we must understand how Information works, how Universe works, and how Mind works. Once we understand how it works, we should master it. When we master Mind, we can pick our interpretation of reality. When we can pick our interpretation of reality, we can shape our reality. When we can shape our reality, we are free.