Employee Benefit Plans (Details) $ in Millions	12 Months Ended
May 28, 2022 USD ($) defined_benefit_plan	May 29, 2021 USD ($)	May 30, 2020 USD ($)
Defined Benefit Plan Disclosure
Number of pension plans \| defined_benefit_plan	1
Pension contributions	$ 5.0	$ 5.4	$ 0.9
Cost recognized	36.3	23.7	$ 22.2
Pension Plan
Defined Benefit Plan Disclosure
Accumulated benefit obligation	$ 250.1	$ 135.5

Defined Benefit Plan, Number of Pension Plans

No definition available.

Name:	mlhr_DefinedBenefitPlanNumberOfPensionPlans
Namespace Prefix:	mlhr_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount of actuarial present value of benefits attributed to employee service rendered, excluding assumptions about future compensation level.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (e)
-URI https://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920

+ Details

Name:	us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_DefinedBenefitPlanDisclosureLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of cost for defined contribution plan.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 70
-Section 50
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=49170846&loc=d3e28014-114942

+ Details

Name:	us-gaap_DefinedContributionPlanCostRecognized
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of cash outflow for pension and other postretirement benefits. Includes, but is not limited to, employer contribution to fund plan asset and payment to retiree.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 25
-Subparagraph (g)
-URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3536-108585

+ Details

Name:	us-gaap_PensionAndOtherPostretirementBenefitContributions
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Details

Name:	us-gaap_RetirementPlanTypeAxis=us-gaap_PensionPlansDefinedBenefitMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: