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Webster 1913 Edition

Noun.

Correction or alteration by writing between the lines; interlineation.

Bp. Burnet.

ppr.

Writing between lines already written or printed.

Noun.

Correction or alteration by writing between the lines.

interlining ‎(plural interlinings)

A cloth lining between the outer and inner layers of a garment.
Correction or alteration by writing between the lines; interlineation.
(Can we find and add a quotation of Bishop Burnet to this entry?)
The scheduling of vehicles to operate more than one route, or the selling of tickets for a trip across multiple carriers

(cloth lining):