Can I (Turkish ) travel to Europe with my husband (British) without a Schengen Visa? [duplicate]

Presuming you have an UK visitor visa you will need a Schengen visitor visa (the UK is not a member of the Schengen area and only a resident visa would extend the fundamental freedom of movement right to you) however this should be quick and easy and even more importantly, free. From Brussels, 19.3.2010 C(2010) 1620 final COMMISSION DECISION of 19.3.2010 establishing the Handbook for the processing of visa applications and the modification of issued visas:

The right of free movement of EU citizens would not have any useful effect without accompanying measures guaranteeing that this right is also given to their families. Therefore the Directive extends the right to free movement to family members of EU citizens. Article 5(2), 2nd sub-paragraph of the Directive provides that “Member States shall grant [family members covered by the Directive] every facility to obtain the necessary visas. Such visas must be issued free of charge as soon as possible and on the basis of an accelerated procedure.