There is a long history between CMMI and ISO standards. CMMI project members have kept abreast of ISO standard development. CMMI and ISO have been compared in articles, mappings, and books ever since CMMI was first published.

CMMI and ISO complement each other. Review some of these publications for more details:

Mapping ISO Standards to CMMI-DEV, V1.2 shows the synergies between CMMI-DEV and three of the most popular ISO standards.

Difference Between CMMI vs. ISO is an analysis posted on Bright Hub that describes how ISO and CMMI differ and are the same.

Process Improvement with CMMI V1.2 and ISO Standards is a 2008 book by Boris Mutafelija and Harvey Stromberg that describes how to use these two standards to improve process quality by quantum leaps.

An Initial Comparative Analysis of the CMMI Version 1.2 Development Constellation and the ISO 9000 Family is an SEI report that enables users of either CMMI or ISO 9000 to learn about the other standard.

CMMI, ITIL & ISO 20000: A Mutually Supportive Relationship, a presentation from SEPG Europe 2009 by Kieran Doyle of Lamri, describes the interrelationships among these three technologies.

Planning a Combined CMMI and AS9100 Appraisal, a presentation from SEPG 2008 by Kevin Schaaff, describes how to combine a CMMI SCAMPI appraisal and and SAE AS9100B audit. 

There are other methods, standards, and technologies that comprise CMMI Compatibility.