The ads continue the "Cravendale tastes so good the cows want it back" television campaign, which broke last December.
The two executions use simple art direction to reflect the purity of the product. The first shows a baby beaker, while the second features a gleaming glass of milk.
Both carry the line "Cravendale fresh milk. Filtered for purity", alongside a shot of the product.
The ads were written by Ben Wade, art directed by Lovisa Algren and photography was by Ben Stockley.
Media planning and buying is through Carat. In the new campaign, a more targeted press campaign replaces mass-market TV.
Ben Scoggins, the DDB account manager on Cravendale, said: "The ads aim to tell mothers that Cravendale is purer than ordinary milk and better for their children because it is extra filtered."
The executions break nationally in magazines in the first week of August.
The first, which targets mothers of younger children, will appear in parenting titles such as BBC Parenting and Mother & Baby. The second, which is aimed at a wider family audience, will be placed in consumer titles such as Eve, Red and BBC Good Food.
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