Is helping my needy husband and my family considered charity from the profits, half of which I vowed to donate as charity?

If your statement: "If the project is completed and starts successfully, I will donate half the profits as charity for Allah" is merely a promise, then it is not considered a binding vow (nadhr). However, if you intended it as a vow, then it is a binding vow that must be fulfilled when its condition is met. If you did not specify a recipient for the vow, it should be given to the needy (masaakeen). If your husband's salary is not sufficient for him, then he is considered needy, and it is permissible for you to give him the charity from the vow. What you previously gave him will not count towards fulfilling the vow unless you intended it as such when you gave it.