Most atheists will affirm the burden of proof lays on the christian since he or she asserts a positive claim, namely God exists. However, no claims can be made in a vacuum. Both the atheist and christian make truth claims either explicitly or implicitly. For example, the atheist affirms metaphysical naturalism and the christian affirms metaphysical supernaturalism. Therefore, both stand in positions of taking on a burden of proof.
If the atheist insists the christian provide evidence for his claims, implicitly the atheist presupposes a criterion for claims, which must be justified, since it is a claim. And thus he is left with the burden of proof of justifying the validity of his criterion for truth. Furthermore, if the atheist demands proof from the christian, the christian can legitimately request the atheist to provide an metaphysical foundation for the epistemic obligation he appeals to when the atheist says, "all rational persons ought to have justification for their claims."
In summary then, there are no neutral positions. The christian and atheist have an epistemic responsibility to justify his/her beliefs. The burden of proof belongs to both the christian and unbeliever.