A person with blue eyes is pure breeding for the blue alleles. This means that he or she can only pass on the blue eyed gene to their offspring. So the child has one blue allele. For this child to have blue eyes he or she needs to inherit a blue eyed allele from the other parent ,in this case you. You obviously have the DOMINANT brown eyed gene and if your baby inherits this it will have brown eyes as brown dominates the blue gene . Your baby can only have blue eyes if you are a carrier for the blue allele and being mixed race you may carry for blue. Even if you do, it is still chance whether the baby will inherit the Dominant brown gene or the (possible) recessive blue gene from you. Hope this makes sense.To summarise your child needs a double copy of blue alleles to be blue phenotype. He/she can only get a double copy if you are carrying one.
