Assalamualaikum,
I work and have my own bank account, but share ownership of the house with my husband. Do I need my own will or the will have to be written jointly with him?

الجواب وباللہ التوفیق
Every person has the right to make a will in his/her possessions and share, and the will is not necessary, however, keeping in mind the circumstances and in view to have ease in the future and the legal complexities, if one takes care of it then it is better. You should write the will of your share and the husband should write of his share.
For further details about the will please see Question number 464.
واللہ اعلم بالصواب