Digital Print...
While Direct Mail is generally more costly per piece due to Design, Paper Costs, The Printing Process, Cutting, Binding, and Shipping / Postage Fees it is also:
Tangible It has as a longer shelf life. (It takes effort to toss a piece of mail that was specifically sent to you with your name on it especially if it is personalized.)
Credible Print gives a sense of legitimacy and authority. (This is the reason many digital marketers also become authors and offer a book as their Tripwire)
Placing ads in publications such as specialty magazines and sending direct mail to targeted lists can effectively reach niche audiences. (Much like running facebook ads with target audiences or buying ad space on a niche blog, or running solo ads in niche specific email lists.)
Print is engaging consumers are more engaged when reading printed material.
Direct Mail engages more of the 5 senses (sight, feel, and sometimes even sound, smell, and taste). The more senses you engage as a marketer the higher the impact on the audience and the more your message will be remembered.
Print also has a linear consumption path (Page after page), Clear reading purpose, Author expertise, Text and Visuals (Pictures, Illustrations)
Digital Marketing...
while many of your marketing messages get lost in a sea of digital messaging on many of your marketing channels, are skimmed and not completely consumed by your target audience before they loose focus and get distracted, and may even have false metrics due to bots, image blocking in emails, spam filters, and cookie blocking, etc.
It is a cheap way to mine and interact with new customers and get your message out to the world quickly and test your audiences interest in new products, services, and promotions.
There are many ways to generate multiple touch points (interactions with your customer) quickly and with pin point targeting accuracy. When these touch points are combined with the Tangible Credibility of Print. You can turbo boost your marketing and become hyper relevant to your customer.
With the invention of Sales Funnels and Cross Media Marketing Campaigns Digital Marketing can also now have the same linear consumption path (page after page), Clear reading and consumption purpose, Author Expertise, Text and Visuals as print with the added benefit of video, sound, and tracking that print doesn't have without Digital Add Ons.
What does a Marketing campaign with both print and digital marketing combined look like?
Much like there are different types of Marketing Campaigns and Sales Funnels being implemented today in different ways and with different Marketing Stacks there is no one way to implement Direct Mail Marketing with Digital Marketing I would have to see your current In House Data (or In House Email and/or mailing List), Live Marketing Campaigns, Print Marketing Collateral, Marketing Stack, etc. and create a Marketing Campaign based on your businesses unique needs and resources.