Map (and Anything) cannot be converted to/from JSON. In essence this is the reason why they cannot be passed between tiers.
Create/Parse JSON do work on both tiers as stated.
If your trouble with JSON is not related to unsupported types, you may have encountered one of a series of JSON related bugs solved in the last few versions, so I suggest you upgrade to the latest (1.3.26 at the moment), and if that does not help, please create a demo project and post it here.
For best results, use the Firefox browser..